Edgar graduated through the Academy ranks at West Ham before joining Leyton Orient and then Barnet, who released him at the end of last season.
And the 23-year-old is keen to kickstart his career again under Daggers boss Wayne Burnett.
"It's good to work with Wayne, we want to push and we want to progress," Edgar told the club's official website. "It's a great place, there's a great team spirit within the team and everyone wants to do well for each other.
"I was at the Peterborough match (a 1-0 defeat in midweek) and think we played some good stuff. We had some great opportunities and we coped well with it and in the end thought we deserved something from the game.
"Wayne's got the team playing a great attacking way, which is one of my main attributes so I can see where I can fit in with the squad. I've heard Wayne speak to the team about what he wants from the players and the attackers and that's right up my street so I think I can fit in well."
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